INTRODUCTION 



The place of estiinates of mortality and replacement in a management 

 program, and their position in the investigation of the pilchard resource 

 of the Pacific coast, are pointed out by Sette (19Ji.3). Derivation of 

 such statistics for fish populations has been investigated by JBaranov 

 (1918), Thompson and Bell (193[i.), and Ricker (19i40), whose theories under- 

 lie the computations described herein. The last named student has de- 

 veloped concepts not included in the v;ork of the earlier authors and 

 gives mathematical formulations in a form more readily adaptable to the 

 data available for the pilchard population than do the others. This 

 report describes the application of Ricker 's formulations to the pilchard 

 data, and also develops nev; equations v/here necessary. To avoid adding 

 to the symbols in the already confused set employed in fisheries statis- 

 tics, those used by Ricker are adapted for this report. 



This analysis was conceived and carried out under the inspiration 

 and guidance of Oscar Elton Sette, in charge. South Pacific Investigations 

 of the United States Fish and V\,''ildlife Service. For critical reading 

 of the manuscript and suggestions for improvement, the author is grateful 

 to Drs. Vit. j5. Ricker, M. 3. Schaefer, J. L. Hart, and Frances N, Clark. 



BASIC ASSUI.1PTI0NS 



In treating fisheries statistics by the method used herein it is 

 necessary to make certain simplifying assumptions. These have been set 

 forth by Ricker (p. UU) and may be condensed as follows: 



1, The amount of effort expended toward catching fish 'is distrib- 

 uted uniformly over the geographical range of the species during 

 the fishing season. 



2. There is no competition between iinits of fishing gear for fish 

 to be caught during one and the same instant. 



Of the two types of fisheries postulated by Ricker, his "Type II" 

 most nearly conforms to that of the pilchard fishery. It differs from 

 his "Type I" in that natural mortality and recruitment take place during 

 the fishing season. The listed assumptions are given by Ricker as ap- 

 plying to his "Type I" fishery, but are later implied to be inherent in 

 "Type II" also (Ricker, I9U0, p. 59). 



They do not hold strictly true for the pilchard fishery, especially 

 with regard to the uniform distribution of fishing effort. This does not 

 preclude the use of the involved formulations, however, if it is kept in 

 mind that they apply only to the extent to which the basic assumptions 

 hold true. 



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